What is 1/32 plus 2/9? (Answer: 73/288)

Exact Answer

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Problem: What is 1/32 plus 2/9?
Formula / Expression: 1/32 + 2/9
Final Answer: 73/288
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 32 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 9 = 288.
Working: LCD(32, 9) = 288

Step 2: Convert to Equivalent Fractions with Common Denominator 288
Multiply the numerator and denominator of 1/32 by 9, and multiply the numerator and denominator of 2/9 by 32 so both fractions share the common base 288.
Working: 1 × 9/32 × 9 = 9/288 and 2 × 32/9 × 32 = 64/288

Step 3: Add the Numerators
Now add the numerators (9 + 64 = 73) and keep the common denominator 288 unchanged.
Working: 9 + 64/288 = 73/288

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 73 and 288 is 1, confirming that 73/288 cannot be reduced further—it is already in its simplest irreducible form.
Working: 73/288

Step 5: Decimal & Percentage Representation
Dividing the numerator 73 by denominator 288 produces a repeating decimal (approximately 0.253472, or 25.3472%).
Working: 73 ÷ 288 = 0.253472 (25.3472%)

Key Values:
- Simplified Fraction: 73/288
- Mixed Number Form: 73/288
- Decimal Value: 0.253472
- Percentage: 25.3472%

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Solved with FractionsCalc:
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1/32 + 2/9 = 73/288

Simplified Fraction

73/288

Mixed Number

Proper (73/288)

Decimal Value

0.253472

Percentage

25.3472%

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Step-by-Step Solution: 1/32 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 32 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 9 = 288.

LCD(32, 9) = 288

Step 2

Convert to Equivalent Fractions with Common Denominator 288

Multiply the numerator and denominator of 1/32 by 9, and multiply the numerator and denominator of 2/9 by 32 so both fractions share the common base 288.

1 × 9/32 × 9 = 9/288 and 2 × 32/9 × 32 = 64/288

Step 3

Add the Numerators

Now add the numerators (9 + 64 = 73) and keep the common denominator 288 unchanged.

9 + 64/288 = 73/288

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 73 and 288 is 1, confirming that 73/288 cannot be reduced further—it is already in its simplest irreducible form.

73/288

Step 5

Decimal & Percentage Representation

Dividing the numerator 73 by denominator 288 produces a repeating decimal (approximately 0.253472, or 25.3472%).

73 ÷ 288 = 0.253472 (25.3472%)

Visual Representation

The diagram below illustrates 1/32 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`73/288`
Mixed Number Form	`73/288`
Decimal Form	`0.253472`
Percentage	`25.3472%`

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Frequently Asked Questions

What is 1/32 plus 2/9 as a fraction?

1/32 + 2/9 in simplest fraction form is 73/288.

What is 1/32 plus 2/9 as a decimal?

1/32 + 2/9 converted to a decimal is 0.253472.

What is 1/32 plus 2/9 as a percentage?

1/32 + 2/9 expressed as a percentage is 25.3472%.

Does 1/32 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.253472...) because the denominator contains prime factors other than 2 and 5.